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Analysis of Fairness-promoting Optimization Schemes of Photovoltaic Curtailments for Voltage Regulation in Power Distribution Networks

Rahul K. Gupta, Daniel K. Molzahn

TL;DR

The paper tackles fairness in PV curtailment for voltage regulation in distribution networks, a problem where PV units receive unequal curtailments due to location. It analyzes two fairness-promoting strategies—adding a fairness objective and employing a past-curtailment-based feedback weighting—and introduces a combined formulation to enable a unified evaluation. Through numerical simulations on benchmark networks, it demonstrates that incorporating fairness (especially with feedback) improves fairness metrics such as the Jain index, and that Pareto analyses reveal trade-offs between fairness and total curtailment under various objective choices. It also highlights that different fairness metrics (e.g., Jain index versus Gini) can yield seemingly conflicting assessments, indicating the need for careful metric selection in practical deployments.

Abstract

Active power curtailment of photovoltaic (PV) generation is commonly exercised to mitigate over-voltage issues in power distribution networks. However, fairness concerns arise as certain PV plants may experience more significant curtailments than others depending on their locations within the network. Existing literature tackles this issue through fairness-promoting/aware optimization schemes. These schemes can be broadly categorized into two types. The first type maximizes an additional fairness objective along with the main objective of curtailment minimization. The second type is formulated as a feedback controller, where fairness is accounted for by assigning different weights (as feedback) in the curtailment minimization objective for each PV plant based on previous curtailment actions. In this work, we combine these two schemes and provide extensive analyses and comparisons of these two fairness schemes. We compare the performance in terms of fairness and net curtailments for several benchmark test networks.

Analysis of Fairness-promoting Optimization Schemes of Photovoltaic Curtailments for Voltage Regulation in Power Distribution Networks

TL;DR

The paper tackles fairness in PV curtailment for voltage regulation in distribution networks, a problem where PV units receive unequal curtailments due to location. It analyzes two fairness-promoting strategies—adding a fairness objective and employing a past-curtailment-based feedback weighting—and introduces a combined formulation to enable a unified evaluation. Through numerical simulations on benchmark networks, it demonstrates that incorporating fairness (especially with feedback) improves fairness metrics such as the Jain index, and that Pareto analyses reveal trade-offs between fairness and total curtailment under various objective choices. It also highlights that different fairness metrics (e.g., Jain index versus Gini) can yield seemingly conflicting assessments, indicating the need for careful metric selection in practical deployments.

Abstract

Active power curtailment of photovoltaic (PV) generation is commonly exercised to mitigate over-voltage issues in power distribution networks. However, fairness concerns arise as certain PV plants may experience more significant curtailments than others depending on their locations within the network. Existing literature tackles this issue through fairness-promoting/aware optimization schemes. These schemes can be broadly categorized into two types. The first type maximizes an additional fairness objective along with the main objective of curtailment minimization. The second type is formulated as a feedback controller, where fairness is accounted for by assigning different weights (as feedback) in the curtailment minimization objective for each PV plant based on previous curtailment actions. In this work, we combine these two schemes and provide extensive analyses and comparisons of these two fairness schemes. We compare the performance in terms of fairness and net curtailments for several benchmark test networks.
Paper Structure (27 sections, 27 equations, 7 figures, 4 tables)

This paper contains 27 sections, 27 equations, 7 figures, 4 tables.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARIES
  3. Grid Model
  4. Photovoltaic Control Model
  5. Demand Model
  6. Voltage Control Problem
  7. FAIRNESS-PROMOTING VOLTAGE CONTROL SCHEMES
  8. Fairness by An Additional Objective Term
  9. Fairness as A Feedback Controller
  10. Combining the Two Formulations
  11. Different Objectives and Fairness Functions
  12. Minimizing the Net Electricity Bill
  13. Not considering past curtailments
  14. Considering past curtailments
  15. Minimize PV Curtailments
  16. ...and 12 more sections

Figures (7)

  • Figure 1: Flow diagram of the different fairness-promoting PV curtailment schemes. Green refers to those with additional fairness objective and green & blue refers to a feedback-based approach along with additional fairness objectives.
  • Figure 2: CIGRE low voltage benchmark network installed with multiple PV plants.
  • Figure 3: Normalized PV generation and load profiles for seven days. This profile is used to generate PV and load generation for each node by multiplying with the nominal capacities.
  • Figure 4: Normalized earnings by exported PV generation with different days of simulations for (a) unfair case and (b) fair case by feedback-based scheme.
  • Figure 5: Normalized PV generation with different days of simulations for (a) unfair case and (b) fair case by feedback-based scheme.
  • ...and 2 more figures